Do not use steel wool. Get those brass curlyQ scrubbing pads from the supermarket. Cut off a section large enough to give a tight fit in the bore when wrapped around an old worn sub-caliber bristle brush and brush back and forth 20-30 times. Extremely fast, effective, and cheap.
If the leading is stubborn and if, and only if, the barrel is stainless steel, mix vinegar and hydrogen peroxide 50/50 plug one end of the barrel and pour in and let sit for 10 min. Be careful not to spill this anywhere else on the gun. Flush and clean. REapply another 10 min if any lead still left. Again, extremely effective and cheap.